Bayesian Learning from Sequential Data Using Gaussian Processes with Signature Covariances
Abstract
We develop a Bayesian approach to learning from sequential data by using Gaussian processes (GPs) with so-called signature kernels as covariance functions. This allows to make sequences of different length comparable and to rely on strong theoretical results from stochastic analysis. Signatures capture sequential structure with tensors that can scale unfavourably in sequence length and state space dimension. To deal with this, we introduce a sparse variational approach with inducing tensors. We then combine the resulting GP with LSTMs and GRUs to build larger models that leverage the strengths of each of these approaches and benchmark the resulting GPs on multivariate time series (TS) classification datasets.
Cite
Text
Toth and Oberhauser. "Bayesian Learning from Sequential Data Using Gaussian Processes with Signature Covariances." International Conference on Machine Learning, 2020.Markdown
[Toth and Oberhauser. "Bayesian Learning from Sequential Data Using Gaussian Processes with Signature Covariances." International Conference on Machine Learning, 2020.](https://mlanthology.org/icml/2020/toth2020icml-bayesian/)BibTeX
@inproceedings{toth2020icml-bayesian,
title = {{Bayesian Learning from Sequential Data Using Gaussian Processes with Signature Covariances}},
author = {Toth, Csaba and Oberhauser, Harald},
booktitle = {International Conference on Machine Learning},
year = {2020},
pages = {9548-9560},
volume = {119},
url = {https://mlanthology.org/icml/2020/toth2020icml-bayesian/}
}